Thursday - June 17, 2010

Cogitatin’ the .45-60

An interior ballistics question

Throat length vs peak pressure in straight walled cases

Take two identical firearms. Chamber one for a straight walled cartridge, and chamber the other one for a longer version of the same cartridge. Assume both chambers are otherwise identical; equally tight or loose. Both firearms have identical barrels that are long enough to allow all the powder to burn before the bullet passes the muzzle.
Examples:
.38 Special and .357 Magnum or .357 Maximum
.45-70 and .45-90
.45-60 and .45-70
.40 S&W and 10mm Magnum
.44 Magnum and .444 Marlin
.458 Win. Magnum and .458 Lott

Cut a perfect close fitting parallel throat in both firearms, but cut the throat longer in the firearm chambered for the shorter cartridge so that the distance from the inside of the case head to the point where the ogive of the bullet contacts the rifling leade is identical.

Choose a bullet that is long enough so that on firing it’s heel is still in the case of the shorter cartridge when the nose contacts the rifling. Let’s assume identical neck tension and crimps too, just to remove those variables from consideration.

Choose a powder charge that is safe and appropriate for the shorter cartridge and bullet and load both cartridges with that bullet, powder charge, and identical primers.

On firing, will both cartridges generate the same peak pressure? The same pressure curve? Or if the pressure curve is skewed on the larger cartridge, which way will it go relative to the smaller one’s curve?

I can see the pressure curve for the longer cartridge being skewed to the right, relative to the curve for the shorter cartridge, since even a full charge of powder in the shorter cartridge will be a less than full charge in the longer case. But my question begs the question of when peak pressures actually occur, relative to the position of the bullet and the friction and other forces acting on it.

Straight walled cases tend to throw nearly all their powder down the barrel as it ignites. They don’t have any of the turbulence benefit that bottleneck cases get, which tends to keep the igniting powder in the case for a longer period of time. All of them are “underbore”, except perhaps for the longest ones of their type (eg .45-120); this means, by volumetric expansion, that they all loose pressure very quickly as the bullet moves down the barrel.

With identical rifling, identical leades, and identical bullets, the engraving force required in both firearms should be identical as well. With matched case head to leade distances, the effective interior volume of both cases is the same at the point in space (and in time?) when the bullets contact the leades. The only difference is that the shorter cartridge may have taken a slightly longer amount of time to push the bullet to that point. A matter of a few microseconds perhaps. Those microseconds give the bullet a slight momentum advantage and allow the shorter cartridge’s powder charge to be a bit more fully burning, but perhaps burning at a lower chamber pressure due to the greater movement of the bullet.  (smokeless powder burns better and faster as the chamber pressure increases) Regardless, once both bullets hit the leades the chamber pressure will start to rise dramatically, since that is the first major bit of friction encountered by the bullets.

[ If you were to build a gun that had a barrel that was only as long as the cartridge case ... the bullet would be sticking out the end of the barrel when it was loaded; the “barrel” would only be the chamber ... when you fired the gun the bullet wouldn’t do much more than pop off the end of the case. You’d have all sorts of burning powder fall out as well. If you built that gun so that it’s barrel was only a chamber and a throat - a bullet diameter smooth tube about 2/3 of a caliber in length - the bullet would pop off going a bit faster, but not by very much. Build that gun with a few inches of actual barrel after that same chamber and throat, and you’ll start to get actual gun-like velocity from that bullet. It takes a bit of time to get the powder burning ( though we are talking about time slices relative to the beginning of what is very nearly an explosion; that bit of time is about 0.0001 seconds), and it takes quite a bit of pressure to make it burn properly. A few inches of rifled barrel give you that pressure because of the radical increase in friction that occurs when you try to cram a metal bullet into a grooved hole of the same or smaller diameter. This is the rifling and the leade (tapered leading edge of the rifling) that I keep referring to. This is why maximum chamber pressure and maximum bullet acceleration always happens in the first few inches of barrel. After that point, internal pressure is actually dropping fiercely, as is the rate of acceleration of the bullet, even though the bullet itself continues to accelerate. With a sufficiently long barrel the relatively constant friction of the bullet moving through the barrel will become greater than the diminishing level of gas pressure within the barrel, and the bullet will actually slow down (it’s rate of acceleration undergoing what mathematics calls a “change of concavity” - it switched from positive to negative), even as the last little bits of the powder are burning up and creating more gas. Here’s a picture:

This is the same exact situation, but looked at from a temporal perspective instead:

PS - these graphs illustrate a puny load. Pressures are usually much higher, and the time elapsed is less than half of this.
PPS - sources tell me it takes about 300 milliseconds to blink your eyes, though I always thought it was 10 times that fast
]

Yes, given sufficiently long barrels, the overall impulse of the powder charges is going to be the same: the areas under the pressure curves will be identical. A given powder charge will always generate the same amount of energy.

In theory a longer throat will always skew a pressure vs time curve to the right, but I don’t know how it will impact overall peak pressures. I have published load data with pressure figures for the longer cartridge, but I’m trying to develop an equal pressure load for the shorter cartridge, for which no published pressure data exists. Finding the peak of that curve is critical, and developing a load that comes near that peak is the object of this exercise. If I knew how the pressure curves related to each other, then load development would be much easier. Especially if it was a simple as their volumetric difference: the .45-60 holds 89% as much powder as the .45-70, so the answer could be a linear application of that ratio. By design the .45-70 does not have much of any kind of a throat. 0.05”. I have been unable to find SAAMI or CIP chamber specifications for the .45-60, but examination of the rifle in question shows that it has a throat about 0.3” long. And that 0.3” is exactly the OAL (OverAll Length) difference between the two cartridges. 

Going the other way, the .45-90 holds 17% more powder then the .45-70. Generally, as case size increases, the burning rate of the best choice powder decreases, so a powder that was a bit fast in the .45-70 will be just right in the .45-60, and one that was a bit slow in the .45-70 will be just right in the .45-90. But these cases aren’t all that different, so many powders should work well in all of them. Longer barrel lengths will mitigate that difference, and tend to favor the slower powders.

The .45-60 and .45-90 are obscure cartridges from long ago, and neither has a big following these days. Thus quality load data in a modern transducer generated format does not exist. Especially at pressure points beyond what the originals were able to generate with black powder. The .45-70 is actually the oldest of the bunch, dating back to 1873, but it has a huge following, and load data exists in 5 or 6 different pressure categories, for 4 different strengths of rifles, from nearly silent roundball loads suitable for rats in your basement right up to magnum loads suitable for elephant hunting. No other cartridge has such a varied categorization. The .45-70 is the definition of arcane, and becomes more so as the pressures increase. But beyond arcane is the land of here there be dragons, the realm of there ain’t no such puppy to be had. And that’s where modern pressure (or even known pressure) smokeless powder loadings for the .45-60 and .45-90 live. Or for custom chambered .45-70s like mine, which actually has a proper tight parallel throat. And I want to go to that realm and plant a flag, but I want to do it safely. This is a no-brainer exercise if you have a proper pressure barrel and a universal receiver and you happen to be White Laboratories. I’m not. And I don’t have the $10,000 that such equipment would cost. Sure, sure, use strain gauges instead. Great idea ... except that they work for round barrels, and the “test bed” rifle in question has an octagonal barrel. So I probably can’t get there that way either. Even having Bergara cut and chamber a custom barrel for a Contender is expensive, plus the strain gauge and software adds another half a thousand. I’d like to find a solution with math, which costs nothing. Except effort and worry.

Posted by Drew458     on 06/17/2010 at 03:22 PM   
Filed Under: • Guns and Gun Control •  
• Comments (13) • Trackbacks(0)  Permalink •  

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